Milnor Fiber Boundary of a Nonisolated Surface Singularity
Authors: Némethi, András, Szilárd, Ágnes
Free Preview Presents a new approach in the study of nonisolated hypersurface singularities
 The first book about nonisolated hypersurface singularities
 Conceptual and comprehensive description of invariants of nonisolated singularities
 Key connections between singularity theory and lowdimensional topology
 Numerous explicit examples for plumbing representation of the boundary of the Milnor fiber Numerous explicit examples for the Jordan block structure of different monodromy operators
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 About this book

In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging nonisolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.
 Reviews

From the reviews:
“The aim of this book is to study the topological types of the oriented smooth 3manifolds appearing as boundaries ∂F of the Milnor fibers of complex surface singularities of embedding dimension 3, as well as the monodromy actions on their homology. … It is clearly invaluable for anybody interested in the topology of nonisolated complex surface singularities and even of singularities of real analytic spaces of dimension 4.” (Patrick PopescuPampu, Mathematical Reviews, January, 2014)
“The book describes three manifolds which occur in relation with complex hypersurfaces in C^{3} near singular points. … I recommend it to all students and researchers who are interested in the local topology of algebraic varieties. It contains a good description of techniques, such as plumbing, cyclic coverings, monodromy, et cetera. The book is well written and ends with several topics for future research.” (Dirk Siersma, Nieuw Archief voor Wiskunde, Vol. 14 (2), June, 2013)
 Table of contents (24 chapters)


Introduction
Pages 17

The Topology of a Hypersurface Germ f in Three Variables
Pages 1115

The Topology of a Pair (f,g)
Pages 1723

Plumbing Graphs and Oriented Plumbed 3Manifolds
Pages 2543

Cyclic Coverings of Graphs
Pages 4554

Table of contents (24 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Milnor Fiber Boundary of a Nonisolated Surface Singularity
 Authors

 András Némethi
 Ágnes Szilárd
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 2037
 Copyright
 2012
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783642236471
 DOI
 10.1007/9783642236471
 Softcover ISBN
 9783642236464
 Series ISSN
 00758434
 Edition Number
 1
 Number of Pages
 XII, 240
 Topics
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